Question

Let $A$ be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a If $P(A)=\frac{11}{36}$, then a is equal to _____

Answer 1

The correct answer is 50.
∣x−y∣<a⇒−a<x−y<a
⇒x−y<a and x−y>−a

P(A)=(OBDF)ar(OACDEG)​
=ar(OBDF)ar(OBDF)−ar(ABC)−ar(EFG)​
⇒3611​=3600(60)2−21​(60−a)2−21​(60−a)2​
⇒1100=3600−(60−a)2
⇒(60−a)2=2500⇒60−a=50
⇒a=10